Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-09T10:28:19.832Z Has data issue: false hasContentIssue false

7 - Iterated forcing and the Continuum Hypothesis

Published online by Cambridge University Press:  05 December 2012

Todd Eisworth
Affiliation:
Ohio University
Justin Tatch Moore
Affiliation:
Cornell University
David Milovich
Affiliation:
University of Wisconsin
James Cummings
Affiliation:
Carnegie Mellon University, Pennsylvania
Ernest Schimmerling
Affiliation:
Carnegie Mellon University, Pennsylvania
Get access

Summary

The ninth Appalachian Set Theory workshop was held at the Fields Institute in Toronto on May 29–30, 2009. The lecturers were Todd Eisworth and Justin Moore. As a graduate student David Milovich assisted in writing this chapter, which is based on the workshop lectures.

The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (primarily in the original edition of [10]) but has proved difficult to read and digest for various reasons. The only new material contained in these lectures concerns the notion of a fusion scheme presented in Sections 6 and 7 and even this has more to do with style than with mathematics. Our presentation of the iteration theorems follows [4]. The k-iterability condition is a natural extrapolation of what appears in [4] and [5], where the iteration theorem for the ℵ0-iterability condition is presented (with a weakening of < ω1-properness). The formulation of complete properness is taken from [8]. We stress, however, these definitions and theorems are really technical and/or stylistic modifications of the theorems and definitions of Shelah presented in [10]. Those interested in further reading on the topic of the workshop should consult: [1], [4], [5], [8], [10], and [12]. We would like to thank Ilijas Farah, Miguel Angel Mota, Paul Shafer, and the anonymous referee for their careful reading and suggesting a number of improvements.

Type
Chapter
Information
Appalachian Set Theory
2006–2012
, pp. 207 - 244
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×